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Search: id:A156170
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| A156170 |
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G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*x^k]^n/n ), a power series in x with integer coefficients. |
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+0
5
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| 1, 1, 3, 10, 41, 219, 1602, 16635, 247171, 5242108, 157390565, 6663089873, 396778864166, 33200932308437, 3906922702271961, 646161881511137940, 150482521507292513413, 49318093291540113084965
(list; graph; listen)
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OFFSET
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0,3
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 41*x^4 + 219*x^5 + 1602*x^6 +...
log(A(x)) = x + 5*x^2/2 + 22*x^3/3 + 117*x^4/4 + 821*x^5/5 + 7796*x^6/6 +...
Log series:
log(A(x)) = Sum_{n>=1} (x + 2^n*x^2 + 3^n*x^3 +...+ k^n*x^k +...)^n/n.
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PROGRAM
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=1, n, k^m*x^k+x*O(x^n))^m/m)), n)}
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CROSSREFS
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Cf. A156171, A155200.
Sequence in context: A030855 A030954 A084786 this_sequence A009329 A009364 A149059
Adjacent sequences: A156167 A156168 A156169 this_sequence A156171 A156172 A156173
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 05 2009
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